I found this site that offers a great articulation of the value of visual data analysis…

Visual statistics, conceptualized as modern successor of epistemology in search for meaning, can help us to separate facts from fiction, has potential to transcend the schism between the quantitative and qualitative approaches to data analysis, and, in general, can contribute to the better understanding of our world. It can offer new algorithms for visualization of data structures rotated in the three-dimensional space, provide us with insights into the hyperspace, and much more.

Quantification and Visualization of Structural Properties

While the primary goal of traditional statistics is to distinguish real differences from random variability, the main goal of visual statistics is not only that, but also the elaboration of these differences into meaningful patterns that can be quantified and visualized. To accomplish this goal, we propose a new conceptualization of variance that encompasses not only the quantification of differences among elements of data matrices into a single index, but also extracts the structural properties of these differences.